Single-mode optical fibres (SMF) are the foundation of high-speed digital communication infrastructure, with a ubiquitous presence in today's interconnected society. They enable internet in our homes and are in submarine cables transferring data between continents. Since the introduction of SMF numerous developments have allowed the capacity of optical communication systems to increase over the years by some 6 orders of magnitude since the initial demonstrations in 1970s: the optical fibre amplifier has removed the need for the electronic repeaters and enabled the amplification of multiple, or multiplexed, signals with a single device; the coherent receiver enabled the use of different degrees of freedom of the optical field to transmit information; and information theory has developed coding schemes that allow an increase in the information carried per second and the correction of errors. Despite all of these, the trend observed during the first 40 years in optical communication systems, where the total throughput of the system was increased year after year, appears to be slowing down. The reason is the nonlinear nature of silica-based single-mode fibres that currently imposes a limit on the information they can carry as a communication channel, by introducing signal distortions that depend on the signal power and optical bandwidth. The limit imposed by fibre nonlinearities is sometimes referred to as the nonlinear Shannon limit or the capacity crunch [1]}, [2]}. Experimental demonstrations such as [3]}, [4]}, [5]} have used a variety of digital signal processing techniques to increase the total system throughput, however, the benefits of these techniques remain relatively limited, and even combined, they are unlikely to satisfy the capacity demands for future networks.
